Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation

Shi Jin; Zihao Tang; Xu Yin; Lei Zhang

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arXiv · 2505.04304

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation

Shi Jin·Zihao Tang·Xu Yin·Lei Zhang

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Abstract

In this paper, we construct quantum circuits for the Black-Scholes equations, a cornerstone of financial modeling, based on a quantum algorithm that overcome the cure of high dimensionality. Our approach leverages the Schr\"odingerisation technique, which converts linear partial and ordinary differential equations with non-unitary dynamics into a system evolved by unitary dynamics. This is achieved through a warped phase transformation that lifts the problem into a higher-dimensional space, enabling the simulation of the Black-Scholes equation on a quantum computer. We will conduct a thorough complexity analysis to highlight the quantum advantages of our approach compared to existing algorithms. The effectiveness of our quantum circuit is substantiated through extensive numerical experiments.

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Shi Jin, Zihao Tang, Xu Yin, Lei Zhang. 2025-05-07. Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation. https://arxiv.org/abs/2505.04304

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